In this study,we theoretically investigate the dynamic indentation for measuring the loss (damping) factor of a linear viscoelastic material from its indentation response.A rigid indenter with arbitrary tip profile is assumed to indent into a viscoelastic substrate with arbitrary shape.We perform a theoretical analysis and identify the conditions under which the loss factor of the material can be determined from the phase angle between the applied harmonic indentation load and the corresponding harmonic displacement,a directly measurable quantity in a dynamic indentation test.To validate the conclusion drawn from our theoretical analysis,a series of numerical experiments are performed,including the spherical indentation of a soft layer with irregular surface morphology bonded to a rigid substrate,a conical indenter with tip defects indenting into a half-spherical particle,and the indentation of porous materials.This study may facilitate the use of the dynamic indentation technique to evaluate the damping properties of linear viscoelastic materials,including some advanced polymers and biological soft tissues.
